Abstract
Recently, spaces of ideal convergent sequences of bounded linear operators were studied by Khan et al. (Numer. Funct. Anal. Optim. 39:1278-1290, 2018). This has motivated us to propose the intuitionistic fuzzy I-convergent double sequence spaces determined by the bounded linear operator. In this paper, we investigate the algebraic and topological properties. We also study the concept of the ideal Cauchy and ideal convergence on the said spaces.
Highlights
1 Introduction Zadeh [27] introduced the concept of fuzzy sets in 1965 and Goguen [6] extended it to Lfuzzy sets
The study of the convergence of sequences in a fuzzy normed space is vital to fuzzy functional analysis, we feel that I-convergence in intuitionistic fuzzy normed space would yield a more general foundation
Statistical convergence and ideal convergence of sequences concerning intuitionistic fuzzy normed space were studied by Mursaleen et al [16, 19]
Summary
Zadeh [27] introduced the concept of fuzzy sets in 1965 and Goguen [6] extended it to Lfuzzy sets. Statistical convergence and ideal convergence of sequences concerning intuitionistic fuzzy normed space were studied by Mursaleen et al [16, 19]. Definition 2.4 ([26]) A sequence y = (yij) is said to be I2-Cauchy, if for each > 0, there exist positive integers m = m( ) and n = n( ) such that the set (i, j) ∈ N × N : |yij – ymn| ≥ ∈ I2.
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